18.758 Representations of Lie Groups almost-a-web-page

David Vogan, 2-243



Blurb describing course pdf.

Lecture delivered at AMS meeting in Raleigh 4/5/09 on computing signatures.

Notes on induced representations pdf. These notes discuss (indirectly) Darij Grinberg's question of why induced representations aren't just defined with some kind of tensor product. There is also an outline of Mackey's construction of unitary induced representations. This last part requires some understanding of invariant measures on homogeneous spaces, and that topic is discussed in more detail here.

Everything else is (for now) imported from the 2006 course, and less relevant for this one. If you'd like to warm up for the 2011 course, you might try the notes on representations of SL(2,R), or the notes on flag varieties.

Notes on representations of SL(2,R) dvi ps pdf

Notes on harmonic analysis on compact groups dvi ps pdf The goal is to describe some formulations of the Peter-Weyl theorem that we will use to construct "Hecke algebras" for studying the representations of real reductive groups.

Notes on flag varieties and representation theory dvi ps pdf An outline of the basic facts about flag varieties (a generalization of Grassmannians), their interpretation in terms of GL(n), generalizations to other groups, and applications to representation theory.

Notes on Lie algebra cohomology dvi ps pdf As I was writing this, I gradually realized that almost everything I wanted to include was already in Knapp's book referenced in the notes. Sigh.

Using the Hochschild-Serre spectral sequence to compute cohomology dvi ps pdf